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Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras. (English. Russian original) Zbl 0536.58007
Funct. Anal. Appl. 17, 273-284 (1983); translation from Funkts. Anal. Prilozh. 17, No. 4, 34-48 (1983).
Three series of finite-dimensional self-adjoint representations are constructed for the associative algebra with quadratic constraints introduced in the previous article [Funct. Anal. Appl. 16, 263-270 (1983; Zbl 0513.58028)]. The representations of the first series are shown to be deformations of the familiar irreducible representations of su(2). Two other series have no analogues in the theory of Lie algebras. The representations are constructed in terms of the shift and multiplication operators in some spaces of theta-functions. Some degenerate cases are also considered.

MSC:
53D50 Geometric quantization
17B35 Universal enveloping (super)algebras
17B15 Representations of Lie algebras and Lie superalgebras, analytic theory
16Gxx Representation theory of associative rings and algebras
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